• Proceedings of the Korea Water Resources Association Conference
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• 1992.07a
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• pp.55-66
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• 1992

The energy and momentum coefficients ${\alpha}$ and ${\beta}$ are measures of homogenerity of velocity distribution in a chanel section. They indicate the effect of energy and momentum transport. However, in most practical applications, they are assumed to be unity due to the difficulty in estimating them. Efforts have been made in this study to estimate these coefficients and to develop equations for practical applications. The Prandtl-von Karman logarithmic equation as being used today has limitations and far-reaching assumptions. Therefore, this paper uses Chiu's velocity distribution equation which seems to be capable of serving as such an alternative, to estimate the velocity distribution and the energy and momentum coefficients, ${\alpha}$ and ${\beta}$ results are compared with those computed by other existing equations. For practical applications, this paper also uses Chiu's equation along with the Mannig's equation to calculate ${\alpha}$, ${\beta}$ without velocity data

• Journal of the Korea Academia-Industrial cooperation Society
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• v.8 no.6
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• pp.1560-1565
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• 2007

In this study, Chiu's velocity distribution equation recently developed from the probability and entropy concepts is used to establish a linkage between the mean velocity obtained from the Manning's equation and the corresponding velocity distribution in a channel cross section. The linkage to be established enables computing the velocity distribution along with the mean velocity, from simple hydraulic data such as Manning's n, hydraulic radius and channel slope irrespective of including sediment or not.

• Proceedings of the KAIS Fall Conference
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• 2007.11a
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• pp.113-115
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• 2007

본 연구에서는 Norman Herrick Brooks의 박사논문(1954)에서 심층적으로 시행한 실험실 실측자료를 사용하여 Manning과 Chiu의 연결고리로 제시한 F(M)과 Manning의 n, R(동수반경), I(수로경사)와 같은 아주 간단한 입력자료 만을 가지고도, 수로수직단면의 전체유속분포를 잘 표현할 수 있으며, 동시에 그동안 취득하기 어려운 최대유속($U_{max}$)도 실측하지 않고 손쉽게 산정할 수 있음을 증명하였다.

• Proceedings of the KAIS Fall Conference
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• 2007.05a
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• pp.104-107
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• 2007

현재까지 수리학 분야에서 가장 많이 회자되고 인용된 공식이 있다면 아마도 1800년에 발표한 Manning의 유속 공식이라고 해도 과언은 아닐 것이다. 그만큼 그 쓰임새가 많았을 뿐만 아니라 사용의 편리생과 정확도에서도 매우 우수하였기 때문일 것이다. 그러나, 아무리 우수한 공식이라도 약점이 있듯이, Manning의 유속공식 역시 조도계수n을 추정하는데 많은 어려움이 있는 것도 주지의 사실이다. 이러한 어려움을 극복하기 위하여, 본 연구에서는 확률통계에서 사용되는 엔트로피 개념을 이용한 3차원 유속분포식인 Chiu의 유속공식을 사용하였다. 그러나 지금까지 실증적으로 Chiu의 유속공식과 Manning땅의 유속공식을 비교분석하였던 논문은 Chiu와 Choo의 논문에서 일부 언급된 것 외 논문에서는 찾아볼 수 없는 것이 현실이다. 따라서 본 연구에서는 하상경사를 임의로 변경 가능한 실험수로를 선택하여 정밀법에 의한 유속측정을 우선 실시하였다. 같은 지점의 같은 단면에서 하상경사(${\Theta}$)가 0.000935부터 0.025794까지 28번의 경사변화를 주고 각 경사마다 유량을 측정하여 28개의 유량측정 데이터를, Chiu의 유속공식과 Manning의 유속공식에 각각 적용하여, Chiu의 M과 Manning의 n사이의 관계뿐만 아니라, 하상경사변화에 따른 관련인자들을 함께 분석하였으며, 실측된 평균유속과도 함께 분석하였다.

• Journal of Environmental Science International
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• v.28 no.6
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• pp.535-544
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• 2019

We computed parameters that affect velocity distribution by applying Chiu's two-dimensional velocity distribution equation based on the theory of entropy probability and acoustic doppler current profiler (ADCP) of Jungmun-stream, Akgeun-stream, and Yeonoe-stream among the nine streams in Jeju Province between July 2011 and June 2015. In addition, velocity and flow were calculated using a surface image velocimeter to evaluate the parameters estimated in the velocity observation section of the streams. The mean error rate of flow based on ADCP velocity data was 16.01% with flow calculated using the conventional depth-averaged velocity conversion factor (0.85), 6.02% with flow calculated using the surface velocity and mean velocity regression factor, and 4.58% with flow calculated using Chiu's two-dimensional velocity distribution equation. If surface velocity by a non-contact velocimeter is calculated as mean velocity, the error rate increases for large streams in the inland areas of Korea. Therefore, flow can be calculated precisely by utilizing the velocity distribution equation that accounts for stream flow characteristics and velocity distribution, instead of the conventional depth-averaged conversion factor (0.85).

• Proceedings of the KAIS Fall Conference
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• 2007.05a
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• pp.99-103
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• 2007

정확하고 신뢰성 높은 유량 자료는 수자원의 정량적인 계획과 관리에 필수적이다. 이를 위하여 Chiu는 기존의 결정론적인 흐름 방향 유속분포식의 한계를 극복할 수 있는 방법으로 확률통계에서 사용되는 엔트로피 개념을 이용한 3차원 유속분포 식을 제안하였고, 이를 실험실 데이터와 자연하천에 적용하여 신뢰성과 정확성을 지속적으로 증명하여 마침내 이에 대한 활용성이 매우 크게 대두되어 Chiu의 유속공식을 적극적으로 사용하고 있는 실정이다. 그러나 지금까지 이론적인 유속 분포식을 검증하기 위하여 단면 형상이 일정한 직사각형이나 사다리꼴 동의 실험수로에서부터 불규칙한 단면 형상을 갖는 자연 하천에 대한 적용을 거의 이루고 있는 실정이나, 하상경사가 변하는 경우에도 엔트로피 파라미터(M)가 이에 대응하여 평형상태에 도달하려고 하는지에 대한 연구는 전무하다. 본 연구에서는 하상경사를 임의로 변경 가능한 실험수로를 선택하여 정밀법에 의한 유속측정을 실시하였다. 같은 지점의 같은 단면에서 하상경사(${\Theta}$)가 0.000935부터 0.025794까지 28번의 경사변화를 주고 각 경사마다 유량을 측정하여 28개의 유량측정 데이터를, Chiu의 엔트로피 유속공식에 적용하여, 평균유속과 최대유속 사이의 관계가 선형관계, 즉 하상경사가 변하는 경우에도 엔트로피 파라미터(M)가 이에 대응하여 평형상태에 도달함을 증명하였다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.4B
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• pp.357-363
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• 2009

When yields the mean velocity of the closed conduit which is used generally, it is available to use Darcy Weisbach Friction Loss Head equation. But, it is inconvenient very because Friction Loss coefficient f is the function of Reynolds Number and Relative roughness (${\varepsilon}$/d). So, it is demanded more convenient equation to estimate. In order to prove the reliability and an accuracy of Chiu's velocity equation from the research which sees hereupon, proved agreement very well about measured velocity measurement data by using Laser velocimeter which is a non-insertion velocity measuring equipment from the closed conduit (Laser Doppler Velocimeter: LDV) and an insertion velocity measuring equipment and the Pitot tube which is a supersonic flow meter (Transit-Time Flowmeters). By proving theoretical linear-relation between maximum velocity and mean velocity in laboratory flume without increase and decrease of discharge, the equilibrium state of velocity in the closed conduit which reachs to equilibrium state corresponding to entropy parameter M value has a trend maintaining consistently this state. If entropy M value which is representing one section is determinated, mean velocity can be gotten only by measuring the velocity in the point appearing the maximum velocity. So, it has been proved to estimate simply discharge and it indicates that this method can be a theoretical way, which is the most important in the future, when designing, managing and operating the closed conduit.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.9 no.1
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• pp.154-159
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• 2008

This study proposes how to decide mean velocity which is one of the very important and efficient discharge measurement in water resources area. In order to achieve this goal, Chiu's velocity distribution equation recently developed from the probability and entropy concepts is used to establish, analyze and compare a linkage between the mean velocity obtained from the Manning's equation which is well known in the world. Besides, it becomes clear that a channel cross section also has a propensity to establish and maintain an equilibrium state that can be measured and classified by a function of entropy M, ratio of mean and maximum velocities irrespective of including sediment or varied channel slope. Therefore, The linkage to be established in this study can be used to compute the cross sectional velocity distribution with the maximum velocity.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.12
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• pp.6558-6564
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• 2013

As the average indicator for amount of water flowing in any cross section of a river, the mean discharge has been reported to be a very important factor for examining water circle constructions in a river basin, the design and construction of a hydraulic structure, and water front area use and management. The stage-discharge curve based on discharge and stage data measured in a normal season were basically derived. Using this derivation, the necessary discharge data was obtained. The values produced in this manner corresponded to the measured data in a uniform flow state well, but showed limited accuracy in a flood season (unsteady flow). In the present paper, the mean velocity in unsteady flow conditions, which exhibited loop form properties, was estimated using the new mean velocity formula derived from Chiu's 2-D velocity. The results of RMSE and Polar graph analyses showed that the proposed equation exhibited approximately nineteen times the accuracy compared to the Manning and Chezy equations.

• Journal of Korea Water Resources Association
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• v.52 no.1
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• pp.83-96
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• 2019

In order to properly manage the river water use, it is necessary to collect reliable data of river water use. However, It is not easy to get credible river water use data in Korea because there are some difficultites in reporting and measuring river water use data. Thus, Han River Flood Control Office has installed and operated measuring facility using V-ADCP on the EOUBO intake open channel in the Gosan-Bongdong station section of the Mankyung river, where the use of agricultural water is large. In this study, the applicability of the V-ADCP velocity profile method was evaluated for real-time river water use. For this reason, the parameter sensitivity of Chiu's 2D velocity distribution equation was analyzed and the optimal parameters based on actual discharge data were calculated. In addition, the characteristics of the velocity profile method were analyzed by comparative evaluation of the rating curve method and the index velocity method.